Main Sequence Star Mass: Star 1, 2 & 3 Comparison

[Sastronaut]

Homework Statement

consider the information given below about three main sequence stars. Star 1 will be a main sequence star for 4.5 billion years. Star 2 has a spectral type of M5. Star 3 has the same luminosity as the Sun. Which has the greatest mass or are they approx. the same?

Homework Equations

The Attempt at a Solution

Spectral class M5 tells me that the star is cool, dim, and small. I know that the sun has been on main sequence longer than 4.5 billion years and will remain on it longer than that. I know that the life time of a star is related to their mass. So after pondering the question i believe the answer is Star 1 b/c it will have a shorter life span than star 2 and 3 which to me indicated it is a relatively more massive star. Though is my thought process correct? Could stars 1, 2, and 3 all have approx the same mass? any help would be great thanks pf!

 

[phyzguy]

Your analysis is correct.

 

[Sastronaut]

the only issue i have is that the luminosity is proportion to AT^4 so star two could be large and hence have more mass...any thoughts? i can say that i there is insufficient info to answer

 

[phyzguy]

Main sequence stars of the same mass all have about the same radius and temperature. So the main sequence star with the same luminosity as the sun has about the same mass as the sun. It's true that a red giant could be spectral type M5 and be larger and have more mass than the sun. But a red giant is not a main sequence star.

 

[D H]

the only issue i have is that the luminosity is proportion to AT^4 so star two could be large and hence have more mass...any thoughts? i can say that i there is insufficient info to answer

That is the best answer (insufficient info). All you know about star 2 is its color, and hence its surface temperature). You don't know whether it is a red dwarf, a red giant, or even a red supergiant.

There is a definitive answer if you know that all three stars are main sequence stars (which is what the title of the thread suggests).

 

[Sastronaut]

Your absolutely correct and I recognized that shortly after posting! thank you DH!